FEBRUARY 14, 2017

Speaker: Jason McCullough, Rider University

Title: Rees-like Algebras and the Eisenbud-Goto Conjecture

Abstract: Regularity is a measure of the computational complexity of a homogeneous ideal in a polynomial ring and thus also a projective variety. There are examples in which the regularity growth is doubly exponential in terms of the degrees of the generators but better bounds were conjectured for "nice" ideals. Together with Irena Peeva, I discovered a construction that overturned some of the conjectured bounds for "nice" ideals - including the long-standing Eisenbud-Goto conjecture. Our construction involves two new ideas that we believe will be of independent interest: Rees-like algebras and step-by-step homogenization. I'll explain the construction and some of its consequences.

Time: Tuesday, February 14, 2017, 11:00 - 11:50 a.m.

Place: Exploratory Hall, room 4106

Refreshments will be served at 10:30 a.m.

Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
Tel. 703-993-1460, Fax. 703-993-1491